Mclellan, Charles H

English

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RESEARCHMEMORANDUM
A METHODFOR INCREASINGTHE EFFECTIVENESSOF STABILIZING
SURFACESAT HIGHSUPERSONICMACHNUMBERS
By Charles H. McLellan
Langley AeronauticalLaboratory
LangleyField, Va
NATIONALADVISORYCOMMITTEE
FORAERONAUT
WASHINGTON
Qy.st 3, 1954
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NACARM L54F21
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ADVISORYCOMMITTEEFORAERONAUTICS
RESEARCHMEMORANDUM
A ME31’HODF RINCREASINGTTIEFFECTIXENESS OFSTABILIZING
SURFACESATHIGHSUPEC30NICMACHNUMBERS
By CharlesH.JkLellan
SUMMARY
Largeincreasesin13ft-curveslopeatlowanglesof attackathigh
supersonicMachnuniberscanbe obtainedby theuseofwedge-shapeairfoil
sections.Theuseofsuchsectionsonthetailsurfacesoperatingat
lowanglesof attackon airplsmesormissilestravelingatthesespeeds
csngreatlydecreasethestabilizing-surfacearearequired.Moderate
increasesinsectioneffectiveness(lift-curveslope)overthatformore
conventionaltailsectio~cambe obtainedwithlittleorno increasein
totaldragbecauseofthedecreased”surfacearea
increasescanbe obtained;however,theywild.be
instabilizing-surfacedrag.
INTRODUCTION
. ..
l
required.Larger
accompaniedby increases
A majorprobleminfllghtatsupersonicspeedsisthedecreasein
Mft-curveslopeof EftingsurfaceswithincreaseinMachnumiberand,
hence,thereductionofstabilityandcontroleffectiveness.Themagni-
tudeofthisproblemisild.ustratedby thefactthatata Machnuder
of7 thelift-curveslopeforthinairfoi~.’”at.1OWanglesofattackis .,
aboutone-sixththevalueobtainedata Machnuniberof1.5. Furthermore,
thevsriationinbodyforcecoefficientswithMachnumiber.canbe an I
adversefactorinthestabilityandcontroloftheairplaneormissile. :
lhcreasingthestabili@by increasingthenumberortheareaofthe
stabilizingsurfacesandtheirmomentarmscansometimesresolvethe
problembutmsyoftenresultinunwieldyandinefficientconfigurations.
Theuseofa simplewedgeforthestabilizingsurfaceappearsto
be onewayto increasetheeffectivenessofthesurfaceathighsuper-
sonicMachnuniberswithoutincreasingthesurfacearea. Smallgainsin
Mft-curveslopehavebeenreportedinreferences1, 2, and 3 by using
smallwedgesinsteadofsharp-trailing-edgeairfoils.However,the
magnitudeoftheincreasesthatcanbeobtainedhasnotbeenade~te~
I
1
,
. -. .-——.—_- ..— -
. — ——. — — —
2 ~’ NACARM L54J?21
tiscussed,particularlywithregardto lsrgewedges.nglesandhighsuper-
sonicMachnumbers.Thepurposeofthisreportthereforeistobring
attentiontothelargebenefitsthatmaybe obtainedfromincreasingthe
wedgeangleof stabilizingsurfaces,particularlyathighsupersonicMach
nunibers.
SYMBOLS
CD
CDi
Cf
CL
c~
L
c
P
pL
m
h
t
M
x
a
8
hag coefficient
inviscidragcoefficient
frictioncoefficient(bothsurfaces)
liftcoefficient
lift-coefficient-curveslope
lift
chord
staticpressure
staticpressureon lowersurface
staticpressure,onuppersurface
basepressure
sbfoilthiclmess
Wch number
distancealongchord
anglebetweenfree-stresmflowandchordline
flowdeflectionangle
Subscripts:
1 conditionsaheadofshock
2 conditionsbehindshock
o conditionat a = 0°
-
NACARM L54F21
BASICCONSIDERATIONS
P
A stabilizingsurfacemustbe abletoproducea largerestoring
momentwhenitis disturbedfrmnalinementwiththestrean.(ToSilll-
plifythediscussion,thefollowingis confinedtoflatplatesandair-
foilswithoutcamber.)Fora givenmomentarm,thevalueof C%?o
determinestheeffectivenessofa surfaceoperatingatlowangles-of
attackinproducinga restoringmoment.
TheM.ftcoefficientons.nairfoilsectioncanbeexpressedas
where pL and ~ me thepressureovertheloweranduppersurfaces.
At zeroangleofattacktheratesof changesof pL - P1 and
w - PI ~th ~g~ ofattackfora s-trical airfoilmsybe assumed
equalbutoppositein sign. Itcanbe shownthat
lL ()P2d—PI
da
fora flatplate
where p2/pl istheratioofthepressurebehind
streampressure.Fora symmetricalirfoilother
theaversgepressureP2 overthesurfacemaybe
doP2—
theshocktothefree-
thantheflatplate
stistitutedfor p2.
()d P2\Pl/Fora flatplate — ‘Zat a=OO isequalto — where 5
da m
K&)
istheflowdeflectionsngle. ~Pl)Abovea Machnunberofabout2, —
d5
fora flatplateisapproximatelyproportionalto theWch numberso
that Cho isapproxhatelyinverselyproportionalto M.
.
.—. -. .—-— —— .—
4 -~ NACARM L54F21
Figure1,whichpresentsgraphicallythewelJknownrelation
()
~ P2
2/
~betweenp PI and 5,showsthattheslopesofthesecurves—db
increasesrapidlyas 5 isincreased,particularlyatthehigherMach
numbers.By addingthiclmess,asina wedgeairfoilsection,the b
ofthesurfacescanbe increasedat a constantangleofattack,thereby
()
P2d—Plgivinga largervalueof db—, andconsequentlya largervalueof Cb“()d ‘~PITheratiooftheslope db atanydeflectionangletothatat 5 = 0°
istheratiooftheeffectivenessofthesurfacetothatofa flatplate
at zeroangleofattack.Theuseofa wedgeairfoil.isthemosteffec-
tivewayofincreasingthesectioneffectivenesssincethedeflection
angleisthenconstantoverthesurfaces.
WEDGEAIRFOILcHmAc!mIsTIcs
‘~fectofWedgeAngleandlkchNuniberonLift-CurveSlope
Thevariationofthesectionlift-curveslopewithMachnumberfor
vsriouswedgehalf-anglesa obtainedfromtheslopesof curves imilsr
to thoseinfigure1 ispresentedinfigure2. Therapiddecreasein
thelift-curveslopefora flatplate,5 = 0°,isreadilyapparentin
thisplot. Thisfigureshowsthatverylargegainscanbe obtainedin
sectionllft-curveslopewithmoderatelys-wedge half-angles.From
thisfigureitispossibletodeterminethewedgeanglesrequiredto
maintaina constantvalueof C% asMachnumberisvaried.TheUft-
Curveslopefora 5-perCen&t~Ck~~ond ~fo~ section(whichaS a
wedge half-angle of2.86°) isalsoincludedinfigure2 toshowthe
variationfora moreconventionalwingsection.
Itmustbe pointedoutthatthesevaluessreinviscidsection
Vsluesl AthighMachnumbersthepresenceoftheboundarylsyerwill
increasethepressuresoverthesurface(refs.3 and4) insuchawsy
asto increasethelift-curveslopesll.ghtly.
Tnanactualapplicationfthesecalculations,plan-formandwing-
bodyinterferenceeffectsmustalsobe considered.tivestigationsat
M= 6.9 (refs.3, 4, and5) haveshownthatas’longastheshockis
attachedtothewingleadingedgethelossesin Mft duetoplan-form
effectsaresmall.UnpublishedresultsobtainedintheLsmgleyn-inch
hypersonictumnelhaveshown4ika~ be expectedtheinterference
.-.
.
NACARM L~F21
effectsaresmallatMachnunibersoftheorderof7.
gationsofinterferencead plan-formeffectsforthe
figurationareadvisable.
5
However,irrvesti-
particularcon-
Theratioofthestabilizing-surfacearearequiredto obtaina
givenstabilizingforcefora wedgetothatrequiredfora flatplate
isequaltothereciprocaloftheratioofthelift-curveslopesofthe
twosurfacesat a = ~o. ThisratioofMft-cwrveslopesistherefore
presentedinfigure3 as a measureoftheeffectivenessof a stabilizing
surface.ItisinterestingtonotethatforMachnumbersabove4 the
valueof ‘% is,forallpracticalpurposes,directly
Cb (flatplate)
proportionaltoI&chnuniber.Valuesofrelativesurfaceffectiveness
ofabout4.4me obtainableat M = 7 withthe15°wedgehsli?-angle.
Similarcurvescanbe constructedforwedgehalf-snglesup to theshock
detachmentangle(40°to45° atlkchnwibersabove4.5) withfargeater
n.
‘%
valuesof
% (flatpla.te)” “
EffectofWedgeAngleandMachNumberonDrag
Thelargeincreasesinlift-curveslopearenotaccomplishedwith-
outsom penalty.Forexample,theinviscidsectiondragwiththelsrge-
anglewedgesismuchhigher‘t&mformoreconventionalsectionsuchas
a 5-percent-thickdouble-wedges ctionwiththemaximumthicknessat
50percentchord.Figure4 showstheinviscidragcoefficientsfor
severalwedgeanglesplottedagainstMachntier fortwoconditionsof
basepressure.As shown,themagnitudeofthebasepressm isnot
importantattheetiremelyhighlb,chnunibers.No attempthasbeen
madeto evaluatethebasepressure.
Itmsybe seenfromfigure4 thattheincreasesin inviscidr~
withwedgeangleexelarge.However,skinfrictionshouldbeincluded
insmydragcomparison.Furthermore,sincethesurfaceareacanbe
decreased.forconstantliftbecauseoftheincreasedC~ with
o
increasing5,theareareductionwithincreasingwedgeangleshouldbe
takenintoaccount.Therefore,infigure5 thetotsldragofthewedge
hasbeendlvidedbythedynamicpressureandtheflat-platearea(which
isheldconstant).Theareaofthewedgeairfoilhasbeendecreasedso
thattheliftandconsequentlytherestoringmomentperdegreewillbe
constant. Thiscurvethereforeindicatesthe
fromtheuseofwedgesurfaces.Theordinate
e----
““”—==
dragp_&alty-thatresults
onthisfigureisequal
6tothedrag
dividedby
NACARM L54F21
coefficientbasedon theactualareaofthewedgesection
c%
n. . Thecalculationshavebeenmadefora
~J-uO(fMtpkte)
laminarflat-platesti-frictioncoefficientof0.00217(twosides).
Theskinfrictiononthewedgewascorrectedforthedifferencein
Reynoldsnumber,Machnumber,anddynamicpressureaheadandbehindthe
shock. Thecalculatedskin-frictioncoefficientincludingthesecor-
rectionsincreaseswithwedgeangle.Sincea laminarflowis consid-
ered,thebasepressurewillprobablybe nearfree-streamyressure.A
basepressurequslto streampressurehasthereforebeenassumedin
thisfigure.
Alsoincludedinthisfigureisthevaluefora ‘j-percent-thick
diamondsection.Fortheparticularconditionsselectedforthiscom-
parisonthetotaldragofthediamondsectionisequaltothatforthe
wedgewith b . 4° sndthegreatereffectivenessofthewedge C(%0 is
1.61timesthe C~ ofthediamonds )ectionresultsin a tailsurface
withonly62percenthearearequiredwitha 5-percent-thickdiamnd
section.Below 5 = 4° thewedgesectionhaslesstotaldragthanthe
disamndsectionandwouldstilJhavea largeadvantagein sizeaswell.
aEreducedragatlowerMachnumberifthewedgeangleisvariable
withJkchnumber.latheactualselectionofwedgeangle,calculations
shouldbe madeoverthecompleteMachnuniber
ofoperationanda determinationofthebase
rangeshouldbe made.
APPIZCATION
andReynoldsnuuiberrange
pressurefortheoperating
h app~cation,thewedgeanglemightbevariedwithMachnumber
asshowninfigure6. A variableanglewedgewouldallowCJ% tobe
continuouslyadjustableinflQht soasto allowthestabilitytobe
vsziedasneededandwouldalJowlowdragstobe obtainedatMch num-
bersbelowthemaximumdesignMachmmiberbecauseuseof a variable
wedgeangleaJlowstheuseofreducedsurfacearea.
Thelargeadvantagesofthewedgesurfacecanonlybe realizedwhen
thestabilizingsurfaceisoperatingatlowsingleswiththestream.If
thesurfacemustoperateatlargeanglesofattackinorderto supply
sufficientlyargeliftcoefficientsomaintaintrim,a simpleflat
platewillhavealreadygainedmuchoftheeffectivenessofthewedge.
Therefore,theusefuhessofthewedgesurfaceismainlyin configura-
tionswheretrimisobtainedatlowangles,suchasthevertical.tail
surfaceor allthetailsurfacesof a co~~nfigurationtravelingtinemly
a ballistictrajectory..-s “7-=-‘“
NACAR.ML54F21 7
Thereductionin sizeofthetailsurfacemaybe importantfromthe
standpointofweightaswelJ_asspacerequiredtohousethemissileor
airplane.Theweightreductionpossiblewiththeuseofwedgesections,
whichmsybe considerablygreaterthantheareareduction,canbe a very
importantfactorinmanycases,particularlysincea forwardshiftin
centerofgratityduetothereducedtailweightwillfurtherdecrease
thestabilizingsurfacesrequired.
CONCLUDINGREMARKS’
Lsrgeincreasesinld.ft-c~ slopeathighsupersonicW h numbers
canbe obtainedby theuseofwedge-shapeairfoilsections.Forexsmple,
4.4timestheflat-plateeffectiveness(lift-curveslope)canbeobtained
witha surfaceusingawedgehaM-sngleofl~”ata Machnumberof7.
The use ofsuchsectionsonthetailsurfaceofairplanesornd.ssiles
travelingatsuchhighspee@ csmgreatlydecreasethestabilizing-
surfacearearequired.Theeffectivenesswillincreaseup tothepoint
of shockdetachment(between40°and45° abovea Machnuniberof4.5 for
a two-dimensionalsurface).b general,thelsrgeincreasein section
effectivenesswillbe accompaniedby lqge increasesin stabilizing-
surfacedrag. However,moderateincreasesinsectioneffectiveness
overthatofmoreconventionaltailsectionscanbe obtainedwithEttle
orno increaseintotaldragsincethegreatereffectivenessallowsa
reductioninthemea requiredtomaintaina stableconfiguration.
Theusefulnessofthewedgesurfaceismainlyin configurations
wheretrimisobtainedat lowanglesof attackonthestabilizingsur-
facessincea surfacesuchasa flatplatewhichoperatesatthehigher
anglesof attackwillpossessmuchoftheeffectivenessof a surface
witha wedgesection.
LangleyAeronauticalLaborato~,
NationalAdtisoryCommitteeforAeronautics,
LangleyField,Va.,June7, 1954.
.
8 NACARM L54F21
1.Jaeger,B.F.,I@her,M. L.,andSchroeder,G.M.: TheAerodynamic
CharacteristicsatSupersonicSpeedsofBlunt-Traillng-EdgeAirfoils
fortheNOTSSmall-CaliberAir-to-AirFolding-FinRocket.NAVORD
Rep.L287(NOTS357), U. S.NavalOral.TestStation,Ihyokern,
Feb.24,1951.
2.Chapman,DeanR.,andKester,RobertH.: EffectofTrailing-EHge
ThiclmessonLiftatSupersonicVelocities.NACARMA52B17,1952.
3. McLel.lan,=kS H.,Bertram,MitchelH.,andlbore,JohnA.: An
InvestigationofFourWingsofSqusrePlanFormata MachNumberof
6.86ti theLangleyI_l-IhchI&personicTunnel.NACARM L51D17,1951.
4. McLellm,CharlesH.: ExploratoryWind-TunnelInvestigationofWings
andBod3esat M = 6.9. Jour.Aero.Sci.,vol.18, no.10,Oct.
1951,pp. 641-648.
5. Ulmann,133wsrdF.,andBertram,MLtchelH.: AerodynamicCharacteris-
ticsofL-ow-Aspect-RatioWingsatHighSupersonic~ h Numbers.
NACARML53D3,1953.
2P NACAFMLfiF21 9
S?h?omDef/ec7t/b7479/e{w&9eHo/&??74J?,6, Z&y
Figurel.-Variationofpressureriseacrosshockforvariouslbchnunibers
anddeflectionsingles.
.._..
y = 1.4.L -- ‘--”L--=-:-3
—.—.. ——-— —---- ———— -— ——
——
10
Figwe 2.- Variationof lift-curveslopeat a = 0° withMachnumberfor
variouswedgehalfangles.
..>>-...“z -. . . >’ ==$
.
.—
II
3
--+.
MJ’’IHI l-l- i-l I I I / - - ~
2? / < “/ e%
I I I
— —
— -
/ I I I I i I I I I I I I I I
Figure3.-Effectof wedge
slopeof wedgesto that
.
6 7 8 9 /0 // B /9
- S%_eom ffuch Number
angleand Machnumberon ratio of Ilft-curve
for a flatplateat zeroangleof attack.
— .—.
12 NACARML54F21
.
Figure4.-Variation
——_ ----
Free-S% M-h
ofinviscidragcoefficientofwedgeswithMach
number.
~,_....- -,:--,:-~
—-—...—— .——
.
II
I
./0
.6%9
.s
.Cw
.09
A?
Figure5.-Variation
s, Gag
of drag for a @ven LLft-curveslopeat a = 0° and
M= 6.9. G
II
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5 /--
0/ I I I I 1 ,1,1 1111 I 1111 1111 I I I I I I I I 1,,11 ,1,11111,11111111 !,,,l ,111 [ Iz 39 6 8 /0 Zo Jo 40 mm
Free - S7rec?m
Figure6.-Ve,riationof wedgehalf
curve
/7uch A4mber
@ with Machnuniberfor two l.i.ft-
slopes.


A method for increasing the effectiveness of stabilizing surfaces at high supersonic Mach numbers

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